An involved source told NFL.com's Albert Breer that Williams and another former Saints assistant, Mike Cerullo, were presented over the last two days and cross-examined by the players' representatives. These meetings were termed as an "arbitration," and additional sessions are scheduled for next week in Washington.

"We got to hear what Gregg had to say," Smith said afterward. "We wanted to make sure we were there just to hear him out."

Smith described the hearing, the third this week overseen by former NFL Commissioner Paul Tagliabue, as "peaceful" and "not awkward."

Smith and Vilma -- along with two former Saints, free-agent defensive lineman Anthony Hargrove and Cleveland Browns linebacker Scott Fujita -- were suspended by the NFL for the Saints' cash-for-hits program that the league says Williams ran from 2009 to 2011.

Smith, suspended for four games, and Vilma, suspended for the entire current season, have been playing while their appeals are pending. Smith later had his suspension reduced to three games.

Smith and Vilma were not required to attend Friday, but they wanted to be in the room when their former coach was questioned.

"We know what we did and know what we didn't do," Smith said. "I mean, we just wanted to be there because it was our right to be there."

Smith and Vilma declined to discuss any details of Friday's hearing. Tagliabue has insisted on keeping the contents of the appeals process private. The hearings this week have been behind closed doors.

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"Paul wants to keep it under wraps, keep everything low-key ... so not really much I can say right now," Vilma said

Neither player was required to attend Friday, but as he left, Vilma said: "Of course it felt good being able to go in there."

"We got to hear what Gregg had to say," Smith said. "We wanted to make sure we were there just to hear him out."

Right from the start, the NFL said Williams was in charge of a pay-for-pain bounty system with the New Orleans Saints. The former defensive coordinator -- who told the league about others' involvement -- was being cross-examined Friday by lawyers for players appealing their suspensions in the case.

Tagliabue and various lawyers declined to comment Thursday or Friday.

The NFL has described Vilma and Smith as ringleaders of a performance pool designed to knock targeted opponents out of games. The league has sworn statements from Williams and Cerullo saying Vilma offered $10,000 to anyone who knocked Minnesota Vikings quarterback Brett Favre out of the NFC Championship Game at the end of the 2009 season.

NFL Commissioner Roger Goodell issued the initial suspensions, which also included a full-season ban for Saints coach Sean Payton.